# Can you find the value of $$f'(20\pi)$$?

Calculus Level 3

Let $$f(x)$$ be a function defined for all $$x\in\mathbb{R}$$ such that $$f(x+y)=f(x)\cdot f(y)$$ for all $$x,y\in\mathbb{R}$$. Let $$f'(0)=18$$ and $$f(20\pi)=\tfrac12$$. What is the value of $$f'(20\pi)$$?

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